By Solomon Lefschetz
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Extra resources for Differential Equations: Geometric Theory, 2nd ed
Example text
A : introduction rules left right A,r - A Ai 11. Unbounded arity connectives A and V are connectives such that NA I__ , An) and V (A 1, ... , An) (written briefly as / \i < n Ai or Vi, n Ai) are formulas whenever Ai 's are formulas. ' A : introduction rules left right A,r - A Ai The height of a decision tree is the maximum length of a path through it. Most often the set Y is just the set 10, 1), in which case the branching program (decision tree) computes a Boolean function. For the first part of the next lemma note that any conjunction in a disjunction (of conjunctions) computing f has to have a literal in common with every disjunction in a conjunction (of disjunctions) computing f. 13. Assume that a function f (xl , ... , is computed by a depth 2 circuit that is a disjunction of conjunctions of arity at most s, and at the same time also by a depth 2 circuit that is a conjunction of disjunctions of arity at most s.